Surface area + expression of a variable from formula - examples
- Cube surface and volume
Find the surface of the cube with a volume of 27 dm3.
The cuboid has a surface area 7705 cm2, the length of its edges are in the ratio 1:4:5. Calculate the volume of the cuboid.
The cube has area of base 225 mm2. Calculate the edge length, volume and area of its surface.
- Prism X
The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm3. What is the area of surface of the prism?
- Sphere A2V
Surface of the sphere is 241 mm2. What is its volume?
- Iron sphere
Iron sphere has weight 100 kg and density ρ = 7600 kg/m3. Calculate the volume, surface and diameter of the sphere.
- Nice prism
Calculate the surface of the cuboid if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm.
- Equilateral cylinder
Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
- Angle of deviation
The surface of the rotating cone is 30 cm2 (with circle base), its surface area is 20 cm2. Calculate the deviation of the side of this cone from the plane of the base.
- Prism - box
The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm3. Calculate the surface of the prism.
- Triangular pyramid
It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm3. What is it content (surface area)?
- Above Earth
To what height must a boy be raised above the earth in order to see one-fifth of its surface.
- Volume and surface
Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm2.
- Cone container
Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
- 3sides prism
The base of vertical prism is an isosceles triangle whose base is 10 cm and the arm is 13 cm long. Prism height is three times the height of base triangle. Calculate the surface area of the prism.
- Surface area
The volume of a cone is 1000 cm3 and the content area of the axis cut is 100 cm2. Calculate the surface area of the cone.
- Cube wall
Calculate the cube's diagonal diagonal if you know that the surface of one wall is equal to 36 centimeters square. Please also calculate its volume.
- Tetrahedral prism - rhomboid base
Calculate the area and volume tetrahedral prism that has base rhomboid shape and its dimensions are: a = 12 cm, b = 70 mm, v_a = 6 cm, v_h = 1 dm.
- Water in aquarium
The aquarium cuboid shape with a length of 25 cm and a width of 30 cm is 9 liters of water. Calculate the areas which are wetted with water.